EECS20N: Signals and Systems

• Home
•  Up to Topics
•  Previous
•  Next

Week 10

• FS coefficients
• Negative freq.
• Transfer function
• Filtering
• Filtering sounds
• Filtering images
• Cascade
• Freq response
• Commutativity
• Feedback
• Freq response

Filtering Sounds

Consider a passage of music, where here we display the Fourier series coefficients for each 16ms segment: If you were able to run applets, you would have a display of sounds.

Below, we have filtered the sound with a lowpass filter that attenuates (decreases the amplitude of) frequency components above 400 Hz:

If you were able to run applets, you would have a display of sounds.

Notice that lowpass filtering makes the music sound muffled. You have no doubt heard muffled sounds in environments that are rich with fabrics or other soft materials. These soft materials absorb high frequency sounds more readily than low frequency sounds, yielding a muffled sound.

Below, we have filtered the same sound with a bandpass filter that attenuates components below 800 and above 1200 Hz:

If you were able to run applets, you would have a display of sounds.

Below, we have filtered the same sound with a highpass filter that attenuates components below 1600 Hz:

If you were able to run applets, you would have a display of sounds.